Physics: Work, Power and Energy

JEE/NEET Physics · Work, Energy & Power series · Part 1 of 8 · All parts →

Push a wall all day — exhausting, but physics says you did ZERO work. Push a trolley the same effort — physics says you did real work. The difference? In physics, 'work' isn't sweat — it's force achieving movement along its own direction. Part 1 of the Work, Energy & Power series — the card that powers the whole chapter.

The Simple Idea: Force × Movement

Work measures transfer of energy by a force. The formula is almost embarrassingly simple — how hard you push × how far the thing moves in the direction you push. One newton of push through one metre = one joule of work. But the strictness hides two traps, and both surprise everyone.

What Each Letter Means

The Angle Rule: Only the Matching Part Counts

Pull a trolley with a slanted rope: only the forward part of your pull moves the trolley forward. The upward part just lightens it (no forward movement from that). cos(angle) keeps exactly the matching part: at 0° (pulling straight along) cos = 1, full work; at 60°, half your force counts; at 90°, cos = 0, nothing counts.

The Zero-Work Surprises

Surprise 1 — pushing a wall: huge force, zero movement → d = 0 → work = 0. Your muscles burn stored energy (that's biology), but no work is done ON the wall.

Surprise 2 — carrying a bag on flat ground: your upward hold-force is perpendicular to your forward walking → angle = 90° → cos = 0 → work by the holding force = zero. The bag moves horizontally; your force points up; they don't match.

Surprise 3 — an orbiting satellite: gravity pulls toward Earth; motion is along the orbit. For a circular orbit they're exactly perpendicular — gravity does zero work on a circular orbit. That's why the ISS never slows down.

Positive and Negative Work

Force along motion (0°): positive work — energy given. Force against motion (180°, like friction on a sliding box): negative work — energy taken away. The sign is bookkeeping of energy flow, and it decides entire questions.

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JEE/NEET Physics · Work, Energy & Power series · Part 2 of 8 · All parts →

A car at 60 km/h needs four times the distance to stop as at 30 km/h. Not twice — four times. That single fact kills accidents, and it comes from one formula: moving energy grows with the SQUARE of speed. Part 2 of the Work, Energy & Power series.

Moving Energy, Simply

Anything moving carries energy of motion — kinetic energy (KE). It depends on mass and speed, but NOT equally: mass counts once, speed counts twice (squared):

Feel the square: a 50 kg cyclist at 10 m/s has 2,500 J; at 20 m/s (only double) — 10,000 J, four times. Triple the speed, nine times the energy.

The Work-Energy Theorem: The Great Shortcut

Why this is gold: Newton's method needs force at every instant. The theorem doesn't — it only needs before and after speeds, whatever complicated path connected them. A curved water slide, a bumpy road, a rollercoaster: total work is the same, and the theorem skips every detail in between.

The v² Law and Road Safety

Stopping means removing all the KE, and brakes remove energy roughly at a steady rate over distance. KE ∝ v², so stopping distance ∝ speed². 30→60 km/h: energy ×4, distance ×4. This one line of physics explains speed limits, school-zone signs, and why 'he was only a bit faster' is never true.

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JEE/NEET Physics · Work, Energy & Power series · Part 3 of 8 · All parts →

Lift a brick to a rooftop — it quietly stores the work you did. Let it go — the stored energy returns as motion. Dams, rollercoasters, archer's bows: all run on this stored energy. Potential energy (PE) is work banked by changing a position — height or stretch. Part 3 of the Work, Energy & Power series.

Height Energy: mgh

Lifting a 1 kg brick up 1 m costs ~10 J — banked as PE, returnable on release. Note h is measured from a zero level you choose (the ground, a table, a roof) — only PE changes are physical, so pick the most convenient zero and stay consistent.

Spring Energy: ½kx²

Stretch a spring double: four times the stored energy. Compress triple: nine times. The square makes spring energy grow brutally — why a fully compressed loaded spring is genuinely dangerous.

Conservative: Path Never Matters

Gravity has a beautiful property: the work it does depends ONLY on height change — not the route. Lift a brick straight up 2 m or carry it up a spiral ramp 2 m: gravity's PE change is identical (mgh both ways). Forces like this are called conservative; they allow the free PE↔KE trading of Part 4. Friction is the opposite: its work depends on path length — energy leaks away and never returns.

The PE ↔ KE Trade

Drop the brick: PE (mgh) converts to KE (½mv²). Swing a pendulum: height energy ↔ motion energy, back and forth. Stretch a bow: your work → spring PE → arrow KE. All day, the universe trades between stored and moving energy — Part 4 makes the ledger exact.

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JEE/NEET Physics · Work, Energy & Power series · Part 4 of 8 · All parts →

Drop anything — a feather (in vacuum) or an elephant — from the same height, and both hit the ground at the same speed. Mass doesn't even enter the answer. That's energy conservation at work: the universe's most reliable bookkeeping. Part 4 of the Work, Energy & Power series.

The One Rule

Read it as a see-saw: what KE loses, PE gains, exactly. Total never changes (with only gravity/springs). With friction, the total still doesn't vanish — it leaks out as heat: mechanical energy lost = friction force × distance slid.

The Famous Result: v = √(2gh), No Mass Anywhere

Drop from height h: mgh = ½mv² → divide both sides by m — mass cancels completely → v = √(2gh). Heavy or light, same landing speed (in vacuum). From 20 m: v = √400 = 20 m/s. From 45 m (with g = 10): 30 m/s. One line, no mass, no time — the most useful result in the chapter.

When Friction Leaks the Ledger

Real slides and roads have friction. The bookkeeping then reads: (KE + PE)_start = (KE + PE)_end + friction × distance. The leak isn't lost — it's heat (why brake discs glow, why rubbing warms hands). Questions love this: 'how far does it slide before stopping?' — the leak formula answers in one line.

The Pendulum's Endless Trade

A pendulum swings because energy endlessly converts: maximum height (all PE, still) → bottom (all KE, fastest) → the other side's height (all PE again). With zero friction it would swing forever; real pendulums leak tiny heat each swing — that's why clocks needed winding.

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JEE/NEET Physics · Work, Energy & Power series · Part 5 of 8 · All parts →

Two students carry the same 20 kg load up the same stairs — identical work. One takes 1 minute, the other takes 10 seconds. Same work, wildly different POWER. Power is the speed of doing work — and it's what engines, motors and athletes are actually rated in. Part 5 of the Work, Energy & Power series.

Power, Simply

Feel the numbers: a phone charger ~20 W, a ceiling fan ~75 W, a microwave ~1,000 W, a car at highway pace ~20,000 W, a cricket ball's throw delivered in 0.1 s ~ 1,000 W momentarily. Horsepower (car specs) = 746 W.

The Two Workhorse Formulas

P = Fv is why cars struggle uphill: at fixed engine power, more needed force (climbing) forces less speed. It's also why you slow down when cycling into a headwind — same legs (power), more force needed, so speed must drop.

Efficiency: Nothing Is 100%

A car engine is ~25-35% efficient (most fuel energy becomes heat); an LED bulb ~40-50% (vs an old filament bulb's ~5% to light); an electric motor ~85-95%. Efficiency questions are pure percentage bookkeeping — keep the 'useful' clear.

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JEE/NEET Physics · Work, Energy & Power series · Part 6 of 8 · All parts →

In every crash — a car wreck, a cricket ball on a bat, two ice pucks — one quantity ALWAYS survives the impact untouched, while another usually dies. Knowing which is which solves every collision question in one line each. Part 6 of the Work, Energy & Power series.

The Survivor: Momentum

Why so unbreakable: it's Newton's third law bookkeeping. During the crash, the two bodies push each other with equal, opposite forces for the same time — the changes cancel exactly. Whatever happens inside the crash (denting, heat, sound), the total motion-quantity is locked.

The Casualty: Kinetic Energy

Unlike momentum, KE is a one-direction street: the crash can convert it into heat, dents, and sound — never back. So the sorting is simple:

Equal Masses in Elastic Hits: The Neat Swap

Beautiful shortcut: equal masses colliding elastically simply exchange velocities. The moving one stops; the stopped one moves off with the first one's speed. Newton's cradle shows it in slow, clicking elegance.

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JEE/NEET Physics · Work, Energy & Power series · Part 7 of 8 · All parts →

Swing a bucket of water over your head — the water stays in. Loop a plane — passengers are pushed into seats, not belts. Both are one rule about the minimum speed at the top of a vertical circle. Part 7 of the Work, Energy & Power series: two classic energy stages every exam loves.

Hooke's Law, Simply

Combined with energy: stretch stores ½kx², and releasing converts it to KE. This pairing (F = kx to find forces; ½kx² to find energy) solves every spring question.

The Vertical Circle's Top Point: The Weak Link

In a vertical circle, the top is the danger point — gravity pulls you toward the centre (helping the circle) and speed is lowest there (energy spent on climbing). The question: how slow can you go at the top and still keep the circle?

The √(gR) Rule, Derived

At the top, gravity pulls down — straight toward the centre. In the most desperate case, gravity alone supplies the entire inward push the circle demands:

Below √(gR), gravity wants more inward pull than the circle's path can provide — the object leaves the circle (water leaves the bucket). At or above it, the track/rotation holds. One number, universal: bucket, plane, rollercoaster, satellite (whose 'circle never fails' because it's always in free fall).

Energy Connects the Levels

To find the minimum launch speed at the BOTTOM for a full loop: bottom speed must be enough to climb 2R and still have √(gR) at top. Energy: ½mv_b² = ½m(gR) + mg(2R) → v_b = √(5gR) — the famous √5, sibling of Part 4's 2.5R height rule (they're the same statement, one in speeds, one in heights).

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JEE/NEET Physics · Work, Energy & Power series · Part 8 of 8 · All parts →

A rocket burns tonnes of fuel, your body runs a marathon on a plate of rice, a dam lights a city — three systems, one ledger. The finale of the Work, Energy & Power series handles the advanced leftovers and hands you the complete formula card.

Variable Forces: The Graph Trick

W = Fd assumed constant force. When the force changes (springs! air drag!), plot force vs distance — the work is the area under the graph. Spring work ½kx² is exactly the triangle under F = kx: ½ × base × height = ½ × x × kx. One picture unifies every variable-force case.

Energy Curves: Reading Stability

Plot a body's PE against position. Valleys = stable equilibrium (pushed away, it rolls back — a ball in a bowl). Hills = unstable (a pencil on its tip — any nudge and it leaves). Flat = neutral (a ball on a table). And a small wiggle at a valley's bottom is automatically simple harmonic motion — the bridge into the next series, Oscillations.

The Human Engine

Your body runs at ~100 W idle, ~400 W walking, ~1,000 W sprinting (elite cyclists touch 1,500 W bursts). A day's food ~9 MJ — roughly a 100 W bulb burning 24 hours. You are, quite literally, a moderately powerful heat engine with excellent snack logistics.

The Energy Economy

Chemical (fuel/food) → heat → motion/electricity, with losses at every step. A power plant: fuel → steam → turbine → electricity ≈ 40% max; an EV battery-to-wheel ≈ 85%; incandescent bulb: 5% light, 95% heat. Every 'energy crisis' discussion and star-rating sticker is this chapter at civic scale.

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